# length of a simple pendulum affects the time

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Introduction

. Plan

Aim

To investigate how the length of a simple pendulum affects the time for a complete swing.

Variables

length

The length of the pendulum has a large effect on the time for a complete swing. As the pendulum gets longer the time increases.

size of swing

Surprisingly, the size of the swing does not have much effect on the time per swing.

mass

The mass of the pendulum also does not affect the time.

air resistance

With a small pendulum bob there is very little air resistance. This can easily be seen because it takes a long time for the pendulum to stop swinging, so only a small amount of energy is lost on each swing. A large and light pendulum bob would be affected by a significant amount of air resistance. This might change the way the pendulum moves.

gravity

The pendulum is moved by the force of gravity pulling on it. On the Moon, where the pull of gravity is less, I would expect the time for each swing to be longer.

Theory

When the pendulum is at the top of its swing it is momentarily stationary. It has zero kinetic energy and maximum gravitational potential energy.

Middle

length | mass | displacement | time (20 swings) |

58 | 5 | 10 | 30.63 |

58 | 25 | 10 | 30.75 |

2. Varying displacement of swing

The size of the swing was changed by a factor of three and this had little effect on the time.

length | mass | displacement | time (20 swings) |

58 | 25 | 10 | 30.94 |

58 | 25 | 30 | 31.33 |

3. Varying length

The length was changed by a factor of two. The time increased as the length increased but by a factor of 1.4 approximately.

length | mass | displacement | time (20 swings) |

30 | 25 | 10 | 22.37 |

58 | 25 | 10 | 30.75 |

From the trial data it is easily seen

Conclusion

Reliability

No significant problems or difficulties were encountered when carrying out this investigation. The accuracy and reliability of the results and conclusions are very good. Within the accuracy of the method used, and for the range of values investigated, it is clear that the time for a complete swing of the pendulum is proportional to the square root of the length.

Improvements

The procedure used was simple and straightforward and no difficulties were encountered. A small improvement could be made to measuring the length of the pendulum. A longer rule, or piece of wood, could be placed level with the point of suspension, and a set square could be placed along the flat side and just touching the bottom of the pendulum. This distance could then be measured more accurately than trying to guess where the middle of the bob is. The diameter of the bob could be accurately measured with some vernier callipers so that the true length of the pendulum could then be calculated.

The thread used was quite stretchy. If the investigation was repeated I would replace it with something more rigid, such as extra strong button thread.

More repeats could be taken but I don't think this would add much to the accuracy of the conclusions.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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## Here's what a star student thought of this essay

### Response to the question

The student answers the question well, he at first explains the theory then makes predictions based on theory. I would recommend this as you get your marks for explaining why something will happen, not just stating it will. This student ...

Read full review### Response to the question

The student answers the question well, he at first explains the theory then makes predictions based on theory. I would recommend this as you get your marks for explaining why something will happen, not just stating it will. This student explains why using theory very well. He makes a table which shows that as length increases so does the time period, and a graph. He also goes further and plots a graph of the time period against the square root of length, to prove that the theory is correct and that T is proportional to the square root of length.

### Level of analysis

The student shows his method well and tries to reduce errors by thinking of how to do his experiment while reducing errors. Which I would recommend always doing as it is best to know what you are doing before you do it, you don't want to be confused as to what to do when you get to the experiment. He takes an appropriate number of repeats making his experiment more reliable. He makes sure to control all variables other than his dependent and independent variables as meant. You must be careful to do this as if you don't you could get incorrect results.

### Quality of writing

His table is clear and plotting his average results on a graph, his results are clearly shown. He plots his independent variable on the y axis and depenent on the x axis as you are meant to. There are very few spelling or grammatical errors.

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Reviewed by jackhli 28/02/2012

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